Finite-element method for time-dependent Maxwell's equations based on an explicit-magnetic-field scheme

Abstract

This paper provides a convergence analysis of the finite-element method for time-dependent Maxwell's equations by means of an explicit-magnetic-field scheme. Error estimates in finite time are given. And it is verified that provided the time-stepsize τ is sufficiently small, the proposed algorithm yields for finite time T an error of O ( hs + τ ) in the L2-norm for the electric field E, the magnetic field H, where h is the mesh size and frac(1, 2) < s {less-than or slanted equal to} 1. In addition, some numerical results are reported in the paper. © 2005 Elsevier B.V. All rights reserved.